pca.py

import numpy as np
import warnings

warnings.filterwarnings("ignore")


class PCA:
    def __init__(self, n_component):
        self.n_component = n_component

    def fit_transform(self, X: np.ndarray):
        '''
        :param X: N x d
        :return: N x n_component
        '''

        N, d = X.shape
        self.mean = np.mean(X, axis=0, keepdims=True)
        X = X - self.mean
        cov = 1 / N * X.T @ X
        eig_value, eig_vector = np.linalg.eig(cov)
        index = np.argsort(eig_value)[::-1]  # descending order
        self.eig_value = eig_value[index]
        self.eig_vector = eig_vector[..., index]
        self.P = eig_vector[..., :self.n_component]

        Y = X @ self.P
        return Y.astype(np.float)

    def transform(self, X):
        return (X @ self.P).astype(np.float)

    def fit_transform_components(self, X, components):
        N, d = X.shape
        mean = np.mean(X, axis=0, keepdims=True)
        X = X - mean
        cov = 1 / N * X.T @ X
        eig_value, eig_vector = np.linalg.eig(cov)
        index = np.argsort(eig_value)[::-1]  # descending order
        eig_value = eig_value[index]
        eig_vector = eig_vector[..., index]

        for n_component in components:
            P = eig_vector[..., :n_component]
            Y = X @ P
            X_rec = Y @ P.T + mean
            yield Y, X_rec

    def reconstruct(self, Y):
        '''
        :param Y: N x n_component
        :return: N x d
        '''
        X = Y @ self.P.T + self.mean
        return X


if __name__ == '__main__':
    specified_labels = [2, 3, 5]
    from utils import common

    mnist_root = '../data/raw_mnist'
    data, label, _, _ = common.load_raw_mnist(mnist_root)
    data, label = common.data_filter(data, label, specified_labels)
    pca = PCA(2)
    pca_data = pca.fit_transform(data)
    common.scatter(pca_data, label, 'PCA Visualization.')